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Homogeneous Randers spaces with isotropic S-curvature and positive flag curvature

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Abstract

In this paper, we will give a complete classification of homogeneous Randers spaces with isotropic S-curvature and positive flag curvature. This results in a large class of Finsler spaces with non-constant positive flag curvature. At the final part of the paper, we prove a rigidity result asserting that a homogeneous Randers space with almost isotropic S-curvature and negative Ricci scalar must be Riemannian.

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Authors and Affiliations

  1. College of Mathematics, Tianjin Normal University, Tianjin, 300387, People’s Republic of China

    Zhiguang Hu

  2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, People’s Republic of China

    Zhiguang Hu & Shaoqiang Deng

Authors
  1. Zhiguang Hu
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  2. Shaoqiang Deng
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Correspondence to Shaoqiang Deng.

Additional information

Supported by NSFC (No. 10671096, 10971104) of China.

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Hu, Z., Deng, S. Homogeneous Randers spaces with isotropic S-curvature and positive flag curvature. Math. Z. 270, 989–1009 (2012). https://doi.org/10.1007/s00209-010-0836-9

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  • DOI: https://doi.org/10.1007/s00209-010-0836-9

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